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Resonant Inelastic X-Ray Scattering (RIXS) experiments on the iron-basedladder BaFe$_2$Se$_3$ unveiled an unexpected two-peak structure associated withlocal orbital ($dd$) excitations in a block-type antiferromagnetic phase. Amixed character between correlated band-like and localized excitations was alsoreported. Here, we use the density matrix renormalization group method tocalculate the momentum-resolved charge- and orbital-dynamical responsefunctions of a multi-orbital Hubbard chain. Remarkably, our resultsqualitatively resemble the BaFe$_2$Se$_3$ RIXS data, while also capturing thepresence of long-range magnetic order as found in neutron scattering, $only$when the model is in an exotic orbital-selective Mott phase (OSMP). In thecalculations, the experimentally observed zero-momentum transfer RIXS peakscorrespond to excitations between itinerant and Mott insulating orbitals. Weprovide experimentally testable predictions for the momentum-resolved chargeand orbital dynamical structures, which can provide further insight into theOSMP regime of BaFe$_2$Se$_3$.

Fingerprints of an Exotic Orbital-Selective Mott Phase in the Block Magnetic State of BaFe$_2$Se$_3$ Ladders